64cos^2(θ)=49

Solution

64 cos^{2} (θ) = 49

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn, θ = 2.63623 \dots + 2 πn, θ = - 2.63623 \dots + 2 πn

Solution steps

64 cos^{2} (θ) = 49

Solve by substitution

cos (θ) = \frac{7}{8}, cos (θ) = - \frac{7}{8}

cos (θ) = \frac{7}{8} : θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn

cos (θ) = - \frac{7}{8} : θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

Combine all the solutions

θ = arccos (\frac{7}{8}) + 2 πn, θ = 2 π - arccos (\frac{7}{8}) + 2 πn, θ = arccos (- \frac{7}{8}) + 2 πn, θ = - arccos (- \frac{7}{8}) + 2 πn

Show solutions in decimal form

θ = 0.50536 \dots + 2 πn, θ = 2 π - 0.50536 \dots + 2 πn, θ = 2.63623 \dots + 2 πn, θ = - 2.63623 \dots + 2 πn

sin^{2} (x) + 2 cos (x) - 2 = 0

2 sin (x) = sec (x)

2 - sin (x) = 2 cos^{2} (x)

- sin (x - \frac{π}{2}) = 1 - sin (x - \frac{3 π}{2})

7 (sin (x)) (cos (x)) + cos^{2} (x) = 1